set up the linear programming problem. Do not solve. A brewery manufactures three types of beer-lite, regular and dark. Each vat of lite beer requires 6 bags of barley, 1 bag of sugar, and 1 bag of hops. Each vat of regular bear requires 4 bags of barley, 3 bags of sugar, and 1 bag of hops. each vat of dark beeer requires 2 bags of barley, 2 bags of sugar, and 4 bags of hops. each day the brewery realizes a profit of $10 per vat of lite beer, $20 per vat of regular beer, and $30 per vat of dark beer. how many vats of lite, regular and dark beer should be brewed in order to maximize profits?

a) write down the linear programming problem, including the objective function and system of linear inequalities that constrain the problem, defining all your variables.